Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theoretical approximation bound. The algorithm ensures that all routing demands are satisfied concurrently, and the overall cost is approximately minimized. We provide both a serial and parallel implementation as well as develop several heuristics used to improve the quality of the solution and reduce running time. We provide computational results on a two sets of well-known benchmarks and show that, with a certain set of heuristics, our new algorithms perform extremely well compared with other integer-programming models. 1